Weird symetry in the weight painting after automatic weight painting is applied
Ok first of all YOU CAN KEEP THE MIRROR MODIFIER.
Here is how it works. (assuming your original model is on the left side)
The Mirror Modifier has only one half of the mesh. In that half you have a vertex group for right and for left (.L and .R) or a symmetric one without any suffix. In Weight Paint Mode you can only paint on the original side. If you want to influence the other side, you need to paint the other group (.R not .L). The mirror modifier will keep the content of both .L and .R for the original side. For the flipped side it will just flip the names. That means .L from the original side will be written to .R in the mirrored side AND .R from the original side will be written to .L in the mirrored side.
Ok now that that is clear and you keep your mirror modifier, I can take some guesses as to what happened.

You could not draw the weight paint. In this case disable the subsurf modifier and the solidify modifier and/or change to a bigger brush or, only if that doesn't help, change to Projected drawing with Front Faces Only disabled. (see the other answer, make sure to switch back after this or you will likely cause a mess at some point without realizing, was there, can not recommend.)
You are only able to draw if you are drawing on the original side. So you can't draw on the .L group to remove the spot on the right. You need to select the .R group and paint on the left side where the spot should appear in that case.
You were drawing on the wrong vertex group. I noticed multiple vertex groups for a lot of bones ending on .001. Make sure you only have one per bone and don't confuse them.

Luckily you seem to understand that by now (https://developer.blender.org/T81252).
So consider this an answer to those people recommending to apply the mirror modifier (@moonboots)!
EDIT: if something behaves weird you can always check weight exactly by going into edit mode, selecting one vertex and looking at the vertex data in the right &quot;N&quot; Panel